read HISTABRUT:
print(`Consider the random variable: `):
print(`the number of occurrences of three consecutive 2's`):
print(`in a (uniformly) drawn n-letter word in the alphabet {1,2} `):
gu:=YofR(GJst({1,2},{[2,2,2]},s,t),s,t[2,2,2],30,n,2,r):
print(`The mean is:`, gu[1]):
print(`The variance is:` , gu[2]):
print(`The asympotics to order 2, of the even alpha coefficients (the (2r)-th moment about the mean divided by the r-th power of the variance) `):
print(`as an expression in n and r is:`):
print(gu[3]):
print(`The asympotics to order 2, of the odd alpha coefficients (the (2r+1)-th moment about the mean divided by the (r+1/2)-th power of the variance) `):
print(`as an expression in n and r is:`):
print(gu[4]):
print(``):
print(`In particular it is (as expected) asymptotically normal, but we have an even finer asympotics for the alpha coefficients. `):
print(`This took `, time(), `seconds . `):
quit: